As heatwaves grow more frequent, longer and more intense under a warming climate, the electricity infrastructure that modern societies depend on is being squeezed from several directions at once. A new study published in Nature Energy quantifies precisely how rising temperatures erode the capacity of European transmission grids, and it points to a sharp national divide: under hundreds of projected heatwave scenarios for 2026 to 2030, the Spanish grid exhibits temperature-induced bottlenecks and load shedding, while the German grid remains comparatively resilient.
The research team, led by Enming Liang with Minghua Chen and Srinivasan Keshav, built a unified computational framework that captures three temperature-dependent effects simultaneously within an alternating-current optimal power-flow formulation: heat-driven increases in electricity demand, derating of generator capacity, and spatially resolved thermal limits on transmission lines. The authors note that existing power-flow models either oversimplify thermal effects or become computationally intractable when those effects are resolved in detail. Their framework, by contrast, couples conductor-level heat-balance physics directly into the grid optimization, allowing bottlenecks to emerge where they actually occur on the network rather than being averaged away.
The technical core of the approach is a temperature-dependent extension of the standard alternating-current optimal power flow, or AC-OPF. Conventional AC-OPF uses static line parameters and fixed transmission limits. In the new formulation, the current flowing through each branch determines Joule heating and conductor temperature, while the resulting temperature-dependent resistance feeds back into line admittance and the power-flow solution. Because conductor temperature, line resistance and power flow are mutually coupled, the researchers developed an iterative procedure, called Iter-OPF, that alternates between solving the nonlinear AC-OPF subproblems and recalculating segment-level heat balances. Each solution uses updated current limits and temperature-dependent resistances, and the resulting currents update segment temperatures for the next iteration. The nonlinear subproblems are solved with the interior-point optimizer IPOPT.
The conductor physics follows the standard steady-state heat-balance equation of IEEE Std 738-2012, which balances convective and radiative heat loss against solar heat gain and Joule heating from the current. Because high-voltage lines typically use multi-bundle conductors whose neighbouring conductors reduce one another’s cooling, the team reduced the convective and radiative cooling terms by a factor of 0.8, guided by finite-element results showing temperature differences of roughly 5 to 25 degrees Celsius among conductors in four-bundle lines. Under a setting of 0.6 metres per second wind speed and 900 watts per square metre of solar irradiance, this corrected four-bundle representation reaches the 90 degree Celsius thermal limit for aluminium conductor steel-reinforced conductors at approximately 25 degrees Celsius ambient temperature, falling between the estimates obtained by treating each conductor independently and by merging the bundle into a single equivalent conductor.
To capture spatially heterogeneous heatwave effects on long transmission lines, the framework segments each line according to its intersections with the grid cells of weather datasets such as ERA5. Segments along the same line share the same power flow and current but have different resistances under their local weather conditions, and the line’s weather-dependent current limit is set by its most restrictive segment, bounded by the represented nominal rating. Generator behaviour is modelled with technology-specific derating curves: gas turbines lose capacity as warmer, less dense input air demands more compression work, nuclear plants derate at high temperatures because of water-cooling constraints, and copper windings lose efficiency as elevated temperatures raise winding resistance. Renewable output is computed from weather data using the Atlite package, and temperature-dependent demand is calibrated with the Demand.ninja methodology using historical ENTSO-E demand profiles.
Future heatwave conditions for 2026 to 2030 were constructed by a morphing approach that transfers the spatial structure and diurnal temperature patterns of historical heatwaves from 2019, 2022 and 2024 onto future reference climate conditions from the bias-corrected CORDEX regional climate model under the RCP 4.5 scenario. The authors are explicit that the resulting scenarios are conditional on both inputs and are used to evaluate grid operation across a range of projected heatwave conditions, not to predict the timing or exact characteristics of individual future events. Future demand was projected with annual growth rates of 1 to 3 percent, representing alternative pathways associated with emerging electricity uses such as artificial intelligence infrastructure, smart homes and electric vehicles.
The analysis was applied to eight Western European systems: Spain, Portugal, France, Italy, Germany, Belgium, the Netherlands and the UK, all of which have been affected by recent major heatwaves. Grid configurations were derived from the open-source PyPSA-Eur model, using clustered networks at 75 percent of the initial 380-kilovolt transmission resolution after historical heatwave baseline checks, a compromise balancing computational efficiency, network fidelity and the risk of artefactual load shedding. Under-construction lines in the public data were retained, but no additional network expansion was optimized, and future generation investment and storage expansion were not modelled. The authors stress that this configuration provides a common baseline for a near-term stress test rather than a forecast of an unchanged future electricity system.
Across the simulated grid configurations, the results reveal substantial national disparities. The Spanish grid exhibits temperature-induced bottlenecks and load shedding under the projected heatwave scenarios, whereas the German grid remains comparatively resilient. Because the clustered public-network representation of the larger country-level systems does not support reliable definition of individual line contingencies, the team applied a fixed 70 percent security margin to transmission-line limits, following its use as an approximation of contingency security in European grid modelling. On the fully specified IEEE 30-bus benchmark, they implemented preventive security-constrained AC-OPF under heatwave conditions with the standard N-1 criterion, requiring all operational limits to hold after any single line outage. Load shedding was represented through slack variables with a large penalty in the objective function, allowing the model to identify when and where the grid cannot meet demand while respecting security constraints.
Energy storage enters the analysis as a sensitivity rather than a forecast. Using the storage locations and capacities represented in the PyPSA-Eur-derived grid data, the simulations adopt an 80 percent initial state of charge as a pre-charged baseline, complemented by sensitivity analyses across initial states of charge from 0 to 100 percent to characterize how the energy available in the represented storage fleet affects load shedding. Storage units are treated as dispatchable generators in each single-snapshot analysis, and the authors note that this sensitivity does not model future storage siting or installed capacity. For the European scenario runs, two Iter-OPF updates were used to balance accuracy and computational cost; validated against fully stabilized solutions, the two-update results differ on average by less than 1 percent in both load-shedding and line-temperature metrics.
The authors frame the statistical summaries carefully: distributions across the projected hourly heatwave scenarios are descriptive, no inferential hypothesis tests are used, and the morphing-generated profiles are deterministic illustrations of the scenario-construction procedure rather than predictions with error bars. They also acknowledge that public-network models can contain local artefacts from imperfectly assigned loads and generators and incomplete urban transmission infrastructure, and that constraints unavailable in the public data are not modelled, although the framework can incorporate operator-specific topology, asset and operational data when available. Their conclusion is that heatwave-aware power-flow analysis uncovers structural bottlenecks that conventional static-limit models miss, and that such analysis should be integrated into grid planning and adaptation as heatwaves intensify under climate change. The project code, including the Iter-OPF implementation and workflows for reproducing the analyses, is publicly available, and all underlying datasets, from PyPSA-Eur grid data and PGLIB-OPF benchmarks to ERA5 weather fields, Copernicus climate projections and ENTSO-E demand statistics, are open-access.
Subject of Research: Modelling heatwave-induced capacity bottlenecks and load shedding in Western European electricity transmission grids
Article Title: Heatwave-induced capacity bottlenecks in European electricity grids
Article References: Liang, E., Chen, M., & Keshav, S. (2026). Heatwave-induced capacity bottlenecks in European electricity grids. Nature Energy. https://doi.org/10.1038/s41560-026-02151-1
Image Credits: AI Generated
DOI: 10.1038/s41560-026-02151-1
Keywords: heatwaves, electricity grids, transmission limits, optimal power flow, load shedding, Spain, Germany, climate change, grid resilience, conductor thermal modelling, PyPSA-Eur, energy modelling
News Source: Denise Maddox. (October 28, 2026). Heatwaves Could Push European Power Grids Toward Their Thermal Limits. Scienmag.
